A054799 Integers n such that sigma(n+2) = sigma(n) + 2, where sigma = A000203, the sum of divisors of n.

3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 434, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487

Offset

1,1

Comments

Only 3 composite numbers are known: 434, 8575, 8825. This sequence is the union of A050507 and A001359.

The terms are also the solutions of A001065(x) = A001065(x+2), where A001065(n) is the sum of proper divisors of n. - Michel Marcus, Nov 14 2014

References

Sivaramakrishnan, R. (1989): Classical Theory of Arithmetical Functions., M.Dekker Inc., New York, Problem 12 in Chapter V., p. 81.

Links

Table of n, a(n) for n=1..51.

Example

n = 434, divisors = {1, 2, 7, 14, 31, 62, 217, 434}, sigma(434) = 768, sigma(436) = 770; n = 8575, divisors = {1, 5, 7, 25, 35, 49, 175, 245, 343, 1225, 1715, 8575}, sigma(8575) = 12400, sigma(8577) = 12402; n = 8825, divisors = {1, 5, 25, 353, 1765, 8825}, sigma(8525) = 10974, sigma(8527) = 10976.

Mathematica

Select[Range[1500], DivisorSigma[1, #+2]==DivisorSigma[1, #]+2&] (* Jayanta Basu, May 01 2013 *)

Prog

(PARI) is(n)=sigma(n+2)==sigma(n)+2 \\ Charles R Greathouse IV, Feb 13 2013

Crossrefs

Cf. A000203, A001359, A050507.

Sequence in context: A329946 A063700 A078859 * A093326 A001359 A096292

Adjacent sequences: A054796 A054797 A054798 * A054800 A054801 A054802

Keyword

nonn

Author

Labos Elemer, May 22 2000

Status

approved